Finite time singularities for a class of generalized surface quasi-geostrophic equations

被引：20

作者：

Dong, Hongjie ^{[1
]}

Li, Dong ^{[2
]}

机构：

[1] Brown Univ, Dept Appl Math, Providence, RI 02912 USA

[2] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 07期

关键词：

Mellin transform; finite-time singularities; quasi-geostrophic equations; global well-posedness;

D O I：

10.1090/S0002-9939-08-09328-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose and study a class of generalized surface quasi-geostrophic equations. We show that in the inviscid case certain radial solutions develop gradient blow-up in finite time. In the critical dissipative case, the equations are globally well-posed with arbitrary H-1 initial data.

引用

页码：2555 / 2563

页数：9

共 50 条

[1] Regularity results for a class of generalized surface quasi-geostrophic equations
Lazar, Omar
Xue, Liutang
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 130 : 200 - 250
[2] On the regularity of a class of generalized quasi-geostrophic equations
Miao, Changxing
Xue, Liutang
JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (10) : 2789 - 2821
[3] Generalized surface quasi-geostrophic equations with singular velocities
Chae, Dongho
Constantin, Peter
Cordoba, Diego
Gancedo, Francisco
Wu, Jiahong
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2012, 65 (08) : 1037 - 1066
[4] Geometric analysis of the generalized surface quasi-geostrophic equations
Bauer, Martin
Heslin, Patrick
Misiolek, Gerard
Preston, Stephen C.
MATHEMATISCHE ANNALEN, 2024, 390 (03) : 4639 - 4655
[5] Finite time singularities in a 1D model of the quasi-geostrophic equation
Chae, D
Córdoba, A
Córdoba, D
Fontelos, MA
ADVANCES IN MATHEMATICS, 2005, 194 (01) : 203 - 223
[6] LONG TIME LOCALIZATION OF MODIFIED SURFACE QUASI-GEOSTROPHIC EQUATIONS
Cavallaro, Guido
Garra, Roberto
Marchioro, Carlo
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2021, 26 (09): : 5135 - 5148
[7] Gevrey regularity for the subcritical dissipative generalized surface quasi-geostrophic equations
Deng, Wen
Paicu, Marius
MATHEMATISCHE ZEITSCHRIFT, 2025, 309 (04)
[8] REGULARITY CRITERIA FOR THE GENERALIZED MAGNETOHYDRODYNAMIC EQUATIONS AND THE QUASI-GEOSTROPHIC EQUATIONS
Fan, Jishan
Gao, Hongjun
Nakamura, Gen
TAIWANESE JOURNAL OF MATHEMATICS, 2011, 15 (03): : 1059 - 1073
[9] On the V-states for the Generalized Quasi-Geostrophic Equations
Zineb Hassainia
Taoufik Hmidi
Communications in Mathematical Physics, 2015, 337 : 321 - 377
[10] On the V-states for the Generalized Quasi-Geostrophic Equations
Hassainia, Zineb
Hmidi, Taoufik
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 337 (01) : 321 - 377

← 1 2 3 4 5 →